ON INTRINSIC LOCALIZED MODES, BREATHERS AND QUODONS. Helsinki, Accelerator Laboratory, Friday, June 12, 2015.

Transcription

1 ON INTRINSIC LOCALIZED MODES, BREATHERS AND QUODONS What are they? Why do they exist? Where do they exist? Do they exist i crystals? ILMs i germaium? Quodos i mica muscovite? Jua FR Archilla Uiversidad de Sevilla Spai Helsiki, Accelerator Laboratory, Friday, Jue 1, 015

2 Discrete breather obtaied with parcas MD code i Ge Foud by M Klopov ad V Hizhyakov usig LAMMPS

3 Slice: discrete breather obtaied with MD i Ge F=15 THz

4 Fourier spectrum of the MD breather i Ge

5 Desity of states for germaium Breather frequecy i Ge

6 So what is a discrete breather? -Localized vibratio i a periodic medium -Two characteristics so far: -Localizatio -Noliear vibratios (some harmoics) -Well defied frequecy outside the phoo spectrum May move Typical eergies: 05-5 ev

7 Are there other oliear itrisic localized etities? Yes: -Solitos -kiks -Crowdios (replacemet collisios cascade) -Solelectros ad polaros -Others: magetic, spis At least they exist i theory ILMs for some is equal to breathers

8 Some basic maths Suppose a 1D system: u W u V u H ) ( ) ( 1 u u u u H 1 0 ) ( Liearized: ) ( u u u u u Dyamical equatios: Trial solutio ) ( e t q i A u Solutios for frequecies ) ( si 4 0 q +1-1

9 Phoos: u = A cos(q -q t )

10 Phoo spectrum

11 Trial solutio for frequecies outside the phoo spectrum Vt t q i Vt A u ; ) ( e ) ( e ) si(q)sih( V )) (1- cos(q)cosh( V 0

12 Frequecy versus localizatio legth The further apart from the phoo bad, the more localizatio

13 Hard potetial (--) / Soft potetial ( ) Hard: frequecy icreases with amplitude/eergy Soft: frequecy decreases with amplitude/eergy

14 Hard breathers / Soft breathers Sometimes we may have both i the same system: As i ClNa structure

15 Necessary coditios for breather existece Noresoace: b phoo bad Noliearity: w b E 0 Sufficiet hardess if above the phoo bad I those coditios theorems stablish that breathers are exact solutios

16 So breathers exist i mathematical models, but do they exist i crystals? I classical molecular dyamics Ni, Nb,Fe, Cu, Ge, Si, NaCl, NaI, V,W, graphee, graphae, carbo aotubes, C 60, With DFT i graphae, Some at fiite temperature Fe 100K, Nb 300K, Not coclusive, but if they exist Most likely: They are ot geeric Few breathers, depedig o the material ad temperatures

17 I the real world? By Mike Russell It helped two persos to get jobs Also i electrical lattices, arrays of Josephso juctios, catilever arrays, waveguide arrays,

18 I crystals: Maley et al, Uraium at K Phys Rev Lett 96, Formatio of a New Dyamical Mode i alpha-uraium Observed by Ielastic X-Ray ad Neutro Scatterig Physical Review B 77, , Itrisic ature of thermally activated dyamical modes i alpha-u: No equilibrium mode creatio by x-ray ad eutro scatterig I germaium? Archilla, Coelho, Auret, Dubiko, Hizhyakov (015) I mica muscovite? Mike Russell, Eilbeck ad coworkers sice 1963

19 Plasma aealig of defects i germaium Copra ICP Ar plasma source Sb-doped Ge Defect detectio by DLTS N Ge =44x10 cm -3 N Sb =103x10 15 cm -3 N T =107x10 14 cm -3 Ge sample with a Au diode

20 Defects i germaium Ca be produced by irradiatio Some vital, some fatal 0

21 Cocetratio of E-ceter before ad after plasma Before plasma After plasma 4eV, 30 miutes More T less effect 8 ev less effect less eergy tha thermal aealig Archilla, JFR, Coelho, SMM, Auret, FD, Dubiko, VI, Hizhyakov, V: Log rage aealig of defects i germaium by low eergy plasma ios Physica D 97, (015) 1

22 Quodos i mica muscovite Positro tracks Produced i the decay of K 40 with 05 MeV 3 per secod per cm 3 Tracks are Fe oxides, magetite FM Russell, From Nature 1967, Nature 16, 907 ; 17, 51 (1967) ad may more

23 Mica muscovite Catio layers K [Si 6 Al ] IV [Al 4 ] VI O 0 (OH) 4 K + K + : D lattice of repulsive particles 3

24 Quodos: quasi oe-dimesioal excitatios of the lattice i mica muscovite Tracks: magetite Fe 3 O 4 Causes 01% Swift particles muos: after eutrio iteractio Positros: decay of 40K 999% ukow: most i lattice close packed directios Aharmoic lattice vibratios?

25 The piece of mica i your hads

26 Experimetal evidece of travellig excitatios i mica muscovite Trajectories were alog lattice directios withi the K + layer Surface bidig eergy of ejected atoms ukow: typical values 3-8 ev Russell, FM, Eilbeck, JC (007) Evidece for movig breathers i a layered crystal isulator at 300K Europhysics Letters 78, 1004, 1-5 7

27 What about charge? Almost all the decay modes of 40 K leave a charge behid, A supersoic crowdio i mica, Archilla et al, i Quodos i Mica, Archilla et al, Eds, Spriger (015)

28 Quodos may have charge (015) -90% of the decay modes leave a positive charge behid (beta decay) - Oly positive swift particles leave tracks - Positros at ear soic speed leave the same tracks tha quodos FM Russell (015), arxiv:

29 May thaks for your attetio Archilla, Russell ad Coelho, Altea, Spai, 013 Coferece: Quodos i mica: oliear localized travellig excitatios i crystals To appear, Spriger 015

30 May thaks for your attetio Archilla, Hizhyakov ad Dubiko, Tartu, Estoia, November 01 Workshop: Lattice solitos ad irradiatio-iduced oliear pheomea i solids,

31 Some bibliography Log rage aealig of defects i germaium by low eergy plasma ios JFR Archilla, SMM Coelho, FD Auret, VI Dubiko ad V Hizhyakov Physica D 97 (015) Ultra-discrete kiks with supersoic speed i a layered crystal with realistic potetials, JFR Archilla, Yu A Kosevich, N Jiméez, V Sáchez-Morcillo ad LM García-Raffi Phys Rev E 91 (015) 091 Reactio rate theory with accout of the crystal aharmoicity VI Dubiko, PA Selyshchev ad JFR Archilla, Phys Rev E 83 (011) Discrete breathers for uderstadig recostructive mieral processes at low temperatures JFR Archilla, J Cuevas, MD Alba, M Narajo ad JM Trillo, J Phys Chem B 110 (006) 411 Haas, M, Hizhyakov, V, Shelka, A, Klopov, M, Sievers, AJ: Predictio of highfrequecy itrisic localized modes i Ni ad Nb Phys Rev B 84, 144,303(1 8) (011)